Fast and Robust Simulation of Atmospheric Phase Screen by Zernike Polynomials with Recursive Radial Formulas

The Zernike polynomial method is extensively used for atmospheric phase screen generation but is limited by insufficient high-frequency components. Calculating higher-order terms introduces challenges in computational efficiency and numerical instability when using the direct method. This paper analyzes these issues and proposes replacing the direct method with recursive radial formulas. We evaluate four recursive algorithms (Barmak’s, q-recursive, Prata’s and Kintner’s) for their performance in phase screen generation, focusing on computational speed and numerical stability. Our results demonstrate that recursive methods achieve a 10–20-times improvement in computational efficiency and maintain numerical stability even for high-order expansions. The main novelty of this study lies in the comprehensive comparison and validation of these recursive strategies for high-accuracy atmospheric phase screen simulation.